Note: Write R code in external R scripts, and use read_chunk() to read them into the current document.

Initial Environment Set-up

The tidyverse package set.

Acquire the Surgical Wait Times Data

Obtain the surgical wait times data from the Nova Scotia Government Open Data Portal.

The data set has been manually updated by Carlo Carandang per the comments in the data analytics report. A detailed algorithm addressing the various strategies to impute the missing values for some features remains to be documented for reproducibility as newer data becomes available.

Load the Surgical Wait Times Data

Wrangle the Data

Load libraries

## Warning: package 'stringr' was built under R version 3.4.3
## Warning: package 'tibble' was built under R version 3.4.3

Determine the feature names.

 [1] Period         Specialty      Procedure      Provider      
 [5] Zone           Facility       Year           Quarter       
 [9] Consult_Median Consult_90th   Surgery_Median Surgery_90th  
 specialty             
                       
 all specialties       
 cardiac               
 dental                
 general               
 neurosurgery          
 obstetrics/gynaecology
 ophthalmology         
 oral and maxillofacial
 oral maxillofacial    
 orthopaedic           
 otolaryngology (ent)  
 plastic               
 thoracic              
 urology               
 vascular

Examine the data set for any missing values.

 feature   missing_count nonmissing_count
 procedure 0             6843            
 specialty 0             6843            
 procedure                            observations
 all                                  296         
 hernia repair  (adult)               185         
 hernia repair - inguinal/femoral     177         
 gallbladder surgery                  166         
 hysterectomy  (cancer not suspected) 159         
 feature        missing_count nonmissing_count
 consult_90th    12           284             
 consult_median  12           284             
 facility         0           296             
 period           0           296             
 procedure        0           296             
 provider         0           296             
 quarter        296             0             
 specialty        0           296             
 surgery_90th     0           296             
 surgery_median   0           296             
 year           296             0             
 zone             0           296             
 specialty              minimum maximum average sigma total observations
 cardiac                 66      198    157      49     702  5          
 dental                 148     1032    327     319    7006 16          
 general                 65     2234    177     298   14432 56          
 neurosurgery           155      949    252     236    3081 10          
 obstetrics/gynaecology  64      882    199     149    9573 41          
 ophthalmology          115     2875    392     497   16779 33          
 oral maxillofacial     171      620    421     159    4332 11          
 orthopaedic            162     1365    662     318   26539 38          
 otolaryngology (ent)   136     1081    390     258   11910 25          
 plastic                151      738    372     186    5598 15          
 thoracic                73      449    179     134    1307  6          
 urology                 61      819    219     170    6002 22          
 vascular               112      685    307     242    2151  6

Visualise the Data

Feature Relationships

## Warning: Removed 12 rows containing missing values (geom_point).

## List of 1
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##   ..$ lineheight   : NULL
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##   ..$ debug        : NULL
##   ..$ inherit.blank: logi FALSE
##   ..- attr(*, "class")= chr [1:2] "element_text" "element"
##  - attr(*, "class")= chr [1:2] "theme" "gg"
##  - attr(*, "complete")= logi FALSE
##  - attr(*, "validate")= logi TRUE

Total Wait Time by Surgical Specialty

Median Wait Time by Surgical Specialty

Wait Time Distribution by Specialty

## Warning: Ignoring 12 observations
## Warning in RColorBrewer::brewer.pal(N, "Set2"): n too large, allowed maximum for palette Set2 is 8
## Returning the palette you asked for with that many colors
## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

## Warning: 'box' objects don't have these attributes: 'text'
## Valid attributes include:
## 'type', 'visible', 'showlegend', 'legendgroup', 'opacity', 'name', 'uid', 'ids', 'customdata', 'hoverinfo', 'hoverlabel', 'stream', 'y', 'x', 'x0', 'y0', 'whiskerwidth', 'boxpoints', 'boxmean', 'jitter', 'pointpos', 'orientation', 'marker', 'line', 'fillcolor', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'hoverinfosrc', 'ysrc', 'xsrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule'

Wait Time Distribution

## Warning: Ignoring 12 observations

Wait Time Distribution2

## Warning: Ignoring 12 observations

Wait Time Distribution3

## Warning: Ignoring 12 observations
skewness(wait_time_distribution_by_specialty$consult_90th, na.rm = TRUE)
## [1] 5.756205
kurtosis(wait_time_distribution_by_specialty$consult_90th, na.rm = TRUE)
## [1] 47.00944
skewness(wait_time_distribution_by_specialty$surgery_90th)
## [1] 2.301818
kurtosis(wait_time_distribution_by_specialty$surgery_90th)
## [1] 8.162021

Build Model

A linear regression model is constructed.

## Warning: package 'broom' was built under R version 3.4.3
## 
## Attaching package: 'purrr'
## The following object is masked from 'package:magrittr':
## 
##     set_names

Model


Call:
lm(formula = specialty90 ~ specialty)

Coefficients:
                    (Intercept)                 specialtycardiac  
                         257.71                          -117.31  
                specialtydental            specialtyneurosurgery  
                         180.16                            50.39  
specialtyobstetrics/gynaecology           specialtyophthalmology  
                         -24.23                           250.74  
    specialtyoral maxillofacial             specialtyorthopaedic  
                         136.10                           440.68  
  specialtyotolaryngology (ent)                 specialtyplastic  
                         218.69                           115.49  
              specialtythoracic                 specialtyurology  
                         -39.88                            15.10  
              specialtyvascular  
                         100.79  

Call:
lm(formula = specialty90 ~ specialty)

Residuals:
    Min      1Q  Median      3Q     Max 
-536.39 -144.57  -66.16   70.76 2366.55 

Coefficients:
                                Estimate Std. Error t value Pr(>|t|)    
(Intercept)                       257.71      38.80   6.643 1.68e-10 ***
specialtycardiac                 -117.31     135.51  -0.866 0.387417    
specialtydental                   180.16      82.30   2.189 0.029447 *  
specialtyneurosurgery              50.39      99.67   0.506 0.613607    
specialtyobstetrics/gynaecology   -24.23      59.68  -0.406 0.685083    
specialtyophthalmology            250.74      63.71   3.935 0.000106 ***
specialtyoral maxillofacial       136.10      95.75   1.421 0.156338    
specialtyorthopaedic              440.68      61.02   7.222 5.19e-12 ***
specialtyotolaryngology (ent)     218.69      69.83   3.131 0.001930 ** 
specialtyplastic                  115.49      84.41   1.368 0.172388    
specialtythoracic                 -39.88     124.72  -0.320 0.749385    
specialtyurology                   15.10      73.05   0.207 0.836358    
specialtyvascular                 100.79     124.72   0.808 0.419727    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 290.3 on 271 degrees of freedom
Multiple R-squared:  0.2383,    Adjusted R-squared:  0.2046 
F-statistic: 7.066 on 12 and 271 DF,  p-value: 3.522e-11
  r.squared adj.r.squared    sigma statistic      p.value df    logLik
1 0.2383158     0.2045881 290.3315  7.065874 3.522272e-11 13 -2006.896
       AIC      BIC deviance df.residual
1 4041.791 4092.877 22843240         271
[1] "NULL Hypothesis:"
[1] "reject"

Prediction Model

                    (Intercept)                specialtycardiac 
                      257.71429                      -117.31429 
                specialtydental           specialtyneurosurgery 
                      180.16071                        50.38571 
specialtyobstetrics/gynaecology          specialtyophthalmology 
                      -24.22648                       250.74026 
    specialtyoral maxillofacial            specialtyorthopaedic 
                      136.10390                       440.68045 
  specialtyotolaryngology (ent)                specialtyplastic 
                      218.68571                       115.48571 
              specialtythoracic                specialtyurology 
                      -39.88095                        15.10390 
              specialtyvascular 
                      100.78571 
 name                            value     
 (Intercept)                      257.71429
 specialtycardiac                -117.31429
 specialtydental                  180.16071
 specialtyneurosurgery             50.38571
 specialtyobstetrics/gynaecology  -24.22648
 specialtyophthalmology           250.74026
 specialtyoral maxillofacial      136.10390
 specialtyorthopaedic             440.68045
 specialtyotolaryngology (ent)    218.68571
 specialtyplastic                 115.48571
 specialtythoracic                -39.88095
 specialtyurology                  15.10390
 specialtyvascular                100.78571
 name                   value     
 intercept               257.71429
 cardiac                -117.31429
 dental                  180.16071
 neurosurgery             50.38571
 obstetrics/gynaecology  -24.22648
 ophthalmology           250.74026
 oral maxillofacial      136.10390
 orthopaedic             440.68045
 otolaryngology (ent)    218.68571
 plastic                 115.48571
 thoracic                -39.88095
 urology                  15.10390
 vascular                100.78571

ANOVA

## Analysis of Variance Table
## 
## Response: specialty90
##            Df   Sum Sq Mean Sq F value    Pr(>F)    
## specialty  12  7147193  595599  7.0659 3.522e-11 ***
## Residuals 271 22843240   84292                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## [1] "Df"      "Sum Sq"  "Mean Sq" "F value" "Pr(>F)"
## [1] "df"     "sumsq"  "meansq" "fvalue" "pr(>f)"
## Analysis of Variance Table
## 
## Response: specialty90
##            df    sumsq meansq fvalue     pr(>f)
## specialty  12  7147193 595599 7.0659 3.5223e-11
## Residuals 271 22843240  84292
## [1] "ANOVA of the linear regression model; NULL Hypothesis:"
## [1] "reject"